How do you simplify fractions such as 64 over 84?

Answer 1

Simple but longer way:

1. Find any common factor of the numerator and the denominator.
2. If it is 1 then stop. You have got the answer.
3. Otherwise divide the numerator and denominator by the common factor.
4. Repeat from 1.

Less simple but shorter way:

1. Find one highest (or greatest) common factor (HCF/GCF).
2. If it is 1 then stop. The fraction IS in its simplest form.
3. Divide numerator and denominator by the HCF.
4. The fraction is now in its simplest form.

Method I

A common factor of 64 and 84 is 2: so 32/42

A common factor of 32 and 42 is 2: so 16/21

The only common factor of 16 and 21 is 1: So answer = 16/21.

Method II

64 = 2*2*2*2*2*2

84 = 2*2*3*7

So HCF(64, 84) = 2*2 = 4

So 64/84 = 16/21.